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Introduction

In the optical microscope, when light from an illumination source passesthrough the condenser and then through the specimen, some of the lightpasses both around and through the specimen undisturbed in its path. Thislight is called direct, undeviated, or non-­diffracted light, and representsthe background light. Some of the light interacting with the specimen is deviated or diffracted.Diffracted light is rendered one-­half wavelength or 180 degrees out of phase with the direct lightthat has passed through without encountering obstacles. The one-­half wavelength out of phase,caused by the specimen itself, enables this light to cause destructive interference with the directlight when both arrive at the intermediate image plane located at the fixed diaphragm of theeyepiece. The eye lens of the eyepiece further magnifies this image, which finally is projectedonto the retina, the film plane of a camera, or the surface of a light-­sensitive digital image sensor.

What has happened is that the direct or undeviated light is projected by the objective and spreadevenly across the entire image plane at the diaphragm of the eyepiece. The light diffracted by thespecimen interferes at the objective rear focal plane (see Figure 1) and is brought into focus atvarious localized places on the same image plane, where the diffracted light causes destructiveinterference and reduces intensity, resulting in the generation of a pattern containing a widespectrum of grayscale values ranging from very dark to very bright. These patterns of light anddark are what we recognize as an image of the specimen. Because our eyes are sensitive tovariations in brightness, the image becomes a more or less faithful reconstitution of the originalspecimen.

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To help understand the basic principles of image formation, it is suggested that the reader try thefollowing exercise and use an object of known periodic structure as a specimen. Theseexperiments are easiest to conduct using a stage micrometer or similar grating of closely spaceddark lines. To proceed, place the finely ruled grating on the microscope stage and bring it intofocus using first a 10x and then the 40x objective. Remove the eyepiece and, in its place, insert aphase telescope so the rear focal plane of the objective can be observed. If the condenseraperture diaphragm is closed most of the way, a bright white central spot of light will appear atthe back of the objective, which is the image of the aperture diaphragm. To the right and left ofthe central spot, a series of diffraction spectra (also images of the aperture diaphragm;; presentedin Figure 1) will be present, each colored blue on the part closest to the central spot and coloredred on the part of the spectrum farthest from the central bright spot (as illustrated in Figure 2). Theintensity of these colored spectra decreases according to how far the spectrum is located fromthe central spot.

Those diffraction spectra that fall near the periphery of the objective are dimmer than those closerto the central spot. The diffraction spectra illustrated in Figure 2 were captured using threedifferent objective magnifications. In Figure 2(b), the diffraction pattern visible at the rear focalplane of the 10x objective contains two diffraction spectra. If the grating is removed from thestage, as illustrated in Figure 2(a), these spectra disappear and only the central image of theaperture diaphragm remains. If the grating is reinserted, the spectra reappear once again. Notethat the spaces between the colored spectra appear dark. Only a single pair of spectra can beobserved if the grating is examined with the 10x objective. In this case, one diffraction spotappears to the left and one appears to the right of the central aperture opening. If the line gratingis examined with a 40x objective (as shown in Figure 2(c)), several diffraction spectra appear tothe left and right of the central aperture. When the magnification is increased to 60x or 63x (andassuming it has a higher numerical aperture than the 40x objective), several additional spectra(see Figure 2(d)) appear to the right and left of those that are visible with the 40x objective inplace.

Because the colored spectra disappear when the grating is removed, it can be assumed that it isthe specimen itself that is affecting the light passing through, thus producing the colored spectra.Furthermore, if the aperture diaphragm is closed down to a very small opening size, we willobserve that objectives of higher numerical aperture grasp more of these colored spectra than doobjectives of lower numerical aperture. The crucial importance of these two concepts forunderstanding image formation will become clear in the ensuing paragraphs. The central spot oflight (image of the condenser aperture diaphragm) represents the direct or undeviated lightpassing through the specimen or around the specimen undisturbed (illustrated in Figure 3(b)). Itis called the 0th or zeroth order. The fainter images of the aperture diaphragm on each side ofthe zeroth order are called the 1st, 2nd, 3rd, 4th, etc. orders respectively, as represented by thesimulated diffraction pattern in Figure 3(a), which would be observed at the rear focal plane of a40x objective. All the captured orders represent, in this case, the diffraction pattern of the linegrating as seen at the rear focal plane of the objective.

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The fainter diffracted images of the aperture diaphragm are caused by diffracted wavefronts,

spread out in fan shape, at each of the openings of the line grating (Figure 3(b)). The blue

wavelengths are diffracted at a lesser angle than the green wavelengths, which are diffracted at

a lesser angle than the red wavelengths. At the rear focal plane of the objective, the blue

wavelengths from each slit interfere constructively to produce the blue area of the diffracted

image of each spectrum or order. The red and green areas (Figure 3(a)) are spaced a bit further,

but arise from the same phenomenon. Where the diffracted wavelengths are one-­half wave out of

step for each of these colors, the waves destructively interfere to give rise to the dark areas

between the spectra or orders. At the position of the zeroth order, all wavelengths from each slit

add constructively. This produces the bright white light you see as the zeroth order (see Figures

2, 3 and 4) at the center of the rear focal plane of the objective.

The closer the spacing of a line grating, the fewer the spectra that will be captured by a given

objective, as illustrated in Figure 4(a-­c). The diffraction pattern illustrated in Figure 4(a) was

captured by a 40x objective imaging the lower portion the line grating in Figure 4(b), where the

slits are closer together. In Figure 4(c), the objective is focused on the upper portion of the line

grating (Figure 4(b)) where the slits are farther apart, and more spectra are captured by the

objective. The direct light and the light from the higher order diffraction maxima are focused by

the objective to form an image in the intermediate image plane at the fixed diaphragm of the

eyepiece. Here the direct and diffracted light rays interfere and are thus reconstituted into the

real, inverted image that is seen by the eye lens of the eyepiece and further magnified. This is

illustrated in Figure 4(d) through Figure 4(g) with two types of diffraction gratings. The square

grid illustrated in Figure 4(d) represents the orthoscopic image of the grid (in effect, the usual

specimen image observed through the eyepieces) as seen through the full aperture of the

objective. The diffraction pattern derived from this grid is shown as a conoscopic image that

would be seen at the rear focal plane of the objective (Figure 4(e)). Likewise, the orthoscopic

image of a hexagonally arranged grid (Figure 4(f)) produces a corresponding hexagonally

arranged conoscopic image (Figure 4(g)) of first order diffraction patterns.

Diffracted Light and Resolution

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Microscope specimens can be considered as complex line or pattern gratings with details and

openings spanning a large range of sizes. This concept of image formation was largely

developed by Ernst Abbe, the famous German microscopist and optics theoretician of the 19th

Century. According to Abbe (his theories are still widely accepted at the present time), the details

of a specimen will be resolved if the objective captures 2 orders of light, such as the 0th order of

the light and at least the 1st order of diffraction. The greater the number of diffracted orders that

gain admittance to the objective, the more accurately the image will represent the original object.

Furthermore, if a medium of higher refractive index than air (such as immersion oil) is used in the

space between the front lens of the objective and the top of the cover slip (as shown for a dry

objective in Figure 5(a)), the angle of the diffracted orders is reduced and the fans of diffracted

light will be compressed. As a result, an oil immersion objective can capture more diffracted

orders and yield better resolution than a dry objective (Figure 5(b)). Compare the captured orders

in Figure 5(a) and 5(b). Moreover, because blue light is diffracted at a lesser angle than green

light or red light, a lens of a given aperture may capture more orders of light when the

wavelengths are in the blue region of the visible light spectrum. These two principles explain the

classic Rayleigh equation often cited as the basis for calculating point-­to-­point resolution in the

microscope:

d (resolution) = 1.22 • (λ/2NA) (1)

where d is the space between two adjacent particles (still allowing the particles to be perceivedas separate), λ is the wavelength of illumination, and NA is the numerical aperture of theobjective. It is assumed that the microscope also is equipped with a condenser with the same

numerical aperture as the objective (without a condenser, the resolution would be half as good

resulting in resolved details that are twice as large). The greater the number of higher diffracted

orders admitted into the objective, the smaller the details of the specimen that can be clearly

separated or resolved. Herein is the value of using high numerical aperture objectives for

examining the smallest possible details in various specimens. Likewise, the shorter the

wavelength of visible light used, the better the resolution. These ideas explain why high

numerical aperture, apochromatic lenses can separate extremely small details in blue light.

Placing an opaque mask at the back of the objective blocks the outermost diffracted orders. This

either reduces the resolution of the grating lines, or any other specimen details, or it destroys the

resolution altogether so that the specimen is not visible. Hence the usual caution not to close

down the condenser aperture diaphragm below the suggested two-­thirds of the objective's

aperture.

Failure of the objective to grasp more than one of the diffracted orders results in an unresolved

image. In a specimen with very minute details, the diffraction fans are spread at a very large

angle, requiring a high numerical aperture objective to capture them. Likewise, because the

diffraction fans are compressed in immersion oil or in water, objectives designed for such use

can give better resolution than dry objectives. If alternate diffracted orders are blocked out (still

assuming the grating as our specimen), the number of lines in the grating will appear doubled (a

spurious resolution). The important caveat is that actions introduced at the rear of the objective

actually determine the eventual image produced. For small details in a specimen (as opposed to

a line grating), the objective projects the direct and diffracted light onto the image plane of the

eyepiece diaphragm in the form of small, circular diffraction patterns known as Airy disks

(illustrated in Figure 6). High numerical aperture objectives capture more of the diffracted orders

and produce smaller size disks than do low numerical aperture objectives. In Figure 6, Airy disk

size is shown steadily decreasing from Figure 6(a) through Figure 6(c). The larger disk sizes in

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Figures 6(a) and (b) are produced by objectives with lower numerical aperture, while the very

sharp Airy disk in Figure 6(c) is produced by an objective of very high numerical aperture.

The resulting image at the eyepiece diaphragm level is actually a mosaic of Airy disks that are

perceived as light and dark regions of the specimen. Where two disks are so close together that

their central bright spots overlap considerably, the two details represented by these overlapping

disks are not resolved or separated and thus appear as one (illustrated in Figure 6(e)). In

contrast, the Airy disks shown in Figure 6(d) are just far enough apart to be resolved. The basic

principle to be remembered is that the combination of direct and diffracted light (or the

manipulation of direct or diffracted light) is critically important in image formation. The key

locations for such manipulation are the rear focal plane of the objective and the front focal plane

of the condenser. This principle is fundamental to most of the contrast improvement methods in

optical microscopy. More important, it is of particular significance at high magnification of small

details close in size to the wavelength of light. Ernst Abbe was a pioneer in developing these

concepts to explain image formation of light-­absorbing or amplitude specimens.

Contributing Authors

Rudi Rottenfusser -­ Zeiss Microscopy Consultant, 46 Landfall, Falmouth, Massachusetts, 02540.

Erin E. Wilson and Michael W. Davidson -­ National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr.,The Florida State University, Tallahassee, Florida, 32310.

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